Behavioral findings in several strategic games indicate that people punish others if they think they are being treated unequally, even at the cost of minimizing their own material payoff. We investigated the primary driving force behind such non-self-regarding behavior, so-called, altruistic cooperation. In all of our studies, a mini ultimatum game was played either one-shot (in Experiment 1a and 1b) or repeatedly (Experiment 2), and rejections of inequitable distribution were taken as a measure of altruistic cooperation. In Experiment 1a, we replicated previous findings indicating that the key mechanism contributing to the emergence of altruistic cooperation is fairness considerations. In Experiment 1b, we delved into the relative importance of two aspects of fairness considerations (i.e., outcome fairness and intentions) and showed that both aspects were effective in determining the level of altruistic cooperation, with the contribution of intentions being more important. In Experiment 2, we investigated the effect of the opportunity for reputation building and future interaction on altruistic cooperation. We found that these factors became influential only when fairness considerations were weakened, particularly, as a result of the removal of the possible intentions behind an offer.